For the \(L^p\) -estimate and existence and uniqueness of solutions to SDEP, BSDEP and FBSDEP, let us mention a few results. Tang and Li [1]} studied the existence and uniqueness of solution to BSDEP in \(L^2\)  space (see also Barles et. al. [2]}). Situ [3]} derived an existence and uniqueness result for the \(L^2\) -adapted solution to BSDEP, where he considered that its terminal time is a bounded random stopping time and the coefficients are non-Lipschitzian. Wu [4]} obtained the existence and uniqueness results of solution to fully coupled FBSDEP in \(L^2\) -space under the monotonicity condition. Then Wu [5]} gave the existence and uniqueness result and a comparison theorem for such equation in stopping time (unbounded) duration. Yin and Mao [6]} dealt with a class of BSDEP with random terminal times and proved the existence and uniqueness result of adapted solution under the assumption of non-Lipschitzian coefficient. Quenez and Sulem [7]} studied some properties of linear BSDEP and also gave the existence and uniqueness of solution to such a BSDEP with general driver in \(L^p\) -space \((p\ge 2)\)  and its \(L^2\) -estimate. Li and Wei [8]} studied some \(L^p\)  \((p\ge 2)\)  estimates for fully coupled FBSDEP which were proved under the monotonicity assumption for arbitrary time intervals and in a small time intervals by assuming that some Lipschitz constants are sufficiently small. Kruse and Popier [9]} gave the existence and uniqueness of solution to a BSDE with Brownian and Poisson noises in a general filtration in \(L^p\) -spaces \((p>1)\) , especially for the case of \(p\in (1,2)\)  which has to be handled carefully, and some mistake was pointed out when \(p<2\) , which was corrected by themselves in [10]}. Yao [11]} studied \(L^p\) -solution \((p\in (1,2))\)  of a multi-dimensional BSDEP whose generator may not be Lipschitz continuous in \((y,z)\)  and obtained its existence and uniqueness of solution with \(p\) -integrable terminal data. Geiss and Steinicke [12]} proved existence and uniqueness of BSDEP allowing the coefficients in the linear growth- and monotonicity-condition for the generator to be random and time-dependent. In the \(L^2\) -case with linear growth, this also generalized the results in [9]}. Confortola [14]} obtained the existence and uniqueness in \(L^p\)  \((p>1)\)  of solution to a BSDE driven by a marked point process on a bounded interval.
